Question

is x - y rational or irrational

Answer 1

Let x and y be non-zero, rational numbers, and let z be an irrational number. In the first column of the table below is an expression. In the second column, determine whether the value of each expression is rational or irrational.

is x - y rational or irrational

Answer 2

Let x and y be non-zero, rational numbers, and let z be an irrational number. In the first column of the table below is an expression. In the second column, determine whether the value of each expression is rational or irrational.

is 3z rational or irrational

Answer 3

Let x and y be non-zero, rational numbers, and let z be an irrational number. In the first column of the table below is an expression. In the second column, determine whether the value of each expression is rational or irrational.

is -2x rational or irrational

Answer 4

Let x and y be non-zero, rational numbers, and let z be an irrational number. In the first column of the table below is an expression. In the second column, determine whether the value of each expression is rational or irrational.

is y + z rational or irrational

Answer 5

The expression x - y can be either rational or irrational, depending on the values of x and y.

Answer 6

If x and y are both non-zero rational numbers, then their difference, x - y, will also be a rational number.
So, x - y is rational.

Answer 7

Since z is an irrational number, any multiple of z (such as 3z) will also be irrational. Therefore, 3z is an irrational number.

Answer 8

If x is a non-zero rational number, then (-2)x is also a rational number. Multiplying a rational number by -2 does not change its rationality, as the result is still expressible as a quotient of two integers. Therefore, -2x is rational.

Answer 9

If y is a non-zero rational number and z is an irrational number, then their sum, y + z, will be an irrational number. Adding a rational number to an irrational number always results in an irrational number. Therefore, y + z is irrational.